M coloring graph backtracking

def graphColoring(graph,k):
    n=len(graph)
    vis={}
    adj={i:[] for i in range(n)}

    for i in range(n):
        for j in range(n):
            if graph[i][j]==1:
                adj[i].append(j)



    def possible(u,i):
        for ver in adj[u]:
            if ver in vis and vis[ver]==i:
                return False
        return True

    def dfs(u):
        if u==n:return True
        for i in range(k):
            if possible(u,i):
                vis[u]=i
                if dfs(u+1):return True
                vis.pop(u)
        return False
    if dfs(0):return 'YES'
    else:return 'NO'